On the Phenomenon of Low-Frequency, Large-Amplitude Oscillations in a High-Dimensional Linear Dynamical System

Abstract

This article provides an explanation of the observed phenomenon on the basis of a complete analytical solution of the system. The solution is constructed in a standard way by reducing the dynamic problem to the problem of eigenvalues and eigenvectors for the system matrix. When solving, we use methods from the theory of orthogonal polynomials. In addition, we discuss two physical interpretations of the system. The connection between these interpretations and the system is established through the Schrödinger variables.